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Math Help - Good with integrals?

  1. #1
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    Mar 2008
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    Good with integrals?

    A 0.1-F capacitor measures 150V across it. At t=0, the capacitor is connected to a source that sends current i=16t/square root of (4t^2+9) amperes through the circuit. Find the voltage across the capacitor when t=2s.

    I think you use this equation, but im not sure.
    Vc=(1/C)xintegral of ixdt
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  2. #2
    Junior Member
    Joined
    Apr 2008
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    Pittsburgh, PA
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    You're completely right.

    Basically, you know the Capacitance, and you're giving the function of current with respect to time. Since I=\frac{\delta Q}{\delta t} you can just Integrate your I function with respect to t.

    \int_0^2{\frac{16t}{\sqrt{4t^2+9}}}

    Just use a simple u substitution so that

    u=4t^2+9 and \delta u=8t

    From there, you can just integrate the function as 2\int_0^2{\frac{1}{\sqrt{u}}}

    and you will end up with the answer 4\sqrt{u}

    Change your u back into 4t^2+9

    Once you plug in your limits of 0 and 2 you will get \frac{4\sqrt{25}}{C}

    You know that C=.1 so your final result should be V=200V
    Last edited by Kalter Tod; April 10th 2008 at 02:26 PM.
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